Consensus-based leader-follower tracking for a network of perturbed diffusion PDEs via local boundary interaction*

A network of agents, modeled by a class of perturbed diffusion partial differential equations, is under investigation. One agent in the network plays the role of leader, and all the remaining "followers" agents are required to asymptotically track the state of the leader. Only boundary sensing of the agent’s state is assumed, and each agent is controlled through the boundary by Neumann-type actuation. The leader communicates with a subset of followers, and communication among followers takes place through a static connected undirected topology. Persistent perturbations, acting at the controlled boundaries of the followers dynamics, are also considered. To achieve global synchronization on the leader profile while rejecting the effect of such matched disturbances, a chattering-free second-order sliding-mode based consensus protocol is proposed. Performance of the proposed nonlinear interaction protocol is analyzed by applying a Lyapunov-based approach, and a simple set of tuning rules, guaranteeing the asymptotic achievement of synchronization, are obtained.